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- Marching_tetrahedra abstract "Marching tetrahedra is an algorithm in the field of computer graphics to render implicit surfaces. It clarifies a minor ambiguity problem of the marching cubes algorithm with some cube configurations.Since more than 20 years have passed from the patent filing date of the marching cubes (June 5, 1985), the original algorithm can be used freely again, adding only the minor modification to circumvent the aforementioned ambiguity in some configurations.In marching tetrahedra, each cube is split into six irregular tetrahedra by cutting the cube in half three times, cutting diagonally through each of the three pairs of opposing faces. In this way, the tetrahedra all share one of the main diagonals of the cube. Instead of the twelve edges of the cube, we now have nineteen edges: the original twelve, six face diagonals, and the main diagonal. Just like in marching cubes, the intersections of these edges with the isosurface are approximated by linearly interpolating the values at the grid points.Adjacent cubes share all edges in the connecting face, including the same diagonal. This is an important property to prevent cracks in the rendered surface, because interpolation of the two distinct diagonals of a face usually gives slightly different intersection points. An added benefit is that up to five computed intersection points can be reused when handling the neighbor cube. This includes the computed surface normals and other graphics attributes at the intersection points.Each tetrahedron has sixteen possible configurations, falling into three classes: no intersection, intersection in one triangle and intersection in two (adjacent) triangles. It is straightforward to enumerate all sixteen configurations and map them to vertex index lists defining the appropriate triangle strips.".
- Marching_tetrahedra thumbnail Marching_tetrahedrons.png?width=300.
- Marching_tetrahedra wikiPageExternalLink DAGSTUHL.1997.10005.
- Marching_tetrahedra wikiPageID "2820936".
- Marching_tetrahedra wikiPageLength "3660".
- Marching_tetrahedra wikiPageOutDegree "16".
- Marching_tetrahedra wikiPageRevisionID "630507794".
- Marching_tetrahedra wikiPageWikiLink Asymptotic_decider.
- Marching_tetrahedra wikiPageWikiLink Category:Computer_graphics_algorithms.
- Marching_tetrahedra wikiPageWikiLink Computer_graphics.
- Marching_tetrahedra wikiPageWikiLink Image-based_meshing.
- Marching_tetrahedra wikiPageWikiLink Implicit_surface.
- Marching_tetrahedra wikiPageWikiLink Isosurface.
- Marching_tetrahedra wikiPageWikiLink Lookup_table.
- Marching_tetrahedra wikiPageWikiLink Marching_cubes.
- Marching_tetrahedra wikiPageWikiLink Normal_(geometry).
- Marching_tetrahedra wikiPageWikiLink Tessellation.
- Marching_tetrahedra wikiPageWikiLink Tetrahedron.
- Marching_tetrahedra wikiPageWikiLink Triangle_strip.
- Marching_tetrahedra wikiPageWikiLink File:Marching_tetrahedrons.png.
- Marching_tetrahedra wikiPageWikiLinkText "Marching tetrahedra".
- Marching_tetrahedra wikiPageWikiLinkText "marching tetrahedra".
- Marching_tetrahedra wikiPageUsesTemplate Template:Refimprove.
- Marching_tetrahedra wikiPageUsesTemplate Template:Reflist.
- Marching_tetrahedra subject Category:Computer_graphics_algorithms.
- Marching_tetrahedra hypernym Algorithm.
- Marching_tetrahedra type Software.
- Marching_tetrahedra type Algorithm.
- Marching_tetrahedra type Redirect.
- Marching_tetrahedra comment "Marching tetrahedra is an algorithm in the field of computer graphics to render implicit surfaces.".
- Marching_tetrahedra label "Marching tetrahedra".
- Marching_tetrahedra sameAs Q3289761.
- Marching_tetrahedra sameAs Marching_tetrahedra.
- Marching_tetrahedra sameAs m.084tsf.
- Marching_tetrahedra sameAs Q3289761.
- Marching_tetrahedra wasDerivedFrom Marching_tetrahedra?oldid=630507794.
- Marching_tetrahedra depiction Marching_tetrahedrons.png.
- Marching_tetrahedra isPrimaryTopicOf Marching_tetrahedra.